--- math-fun-request@mailman.xmission.com wrote:
From: Marc LeBrun <mlb@fxpt.com> Subject: Re: [math-fun] perfect squares [snip] BTW I've shared RCS's interesting experience of the surprising messiness of such algorithms, such as determining whether p+qx < r+sx for signed p,q,r,s using only integer operations. Heck, I'd even pay $50 for an easy way to generate a+bx in increasing order for a,b >=0 (if you think you have one contact me to negotiate the definition of "easy"<;-).
Fool's errand, if I understand correctly. For any terms p+qx < r+sx, there exists an u s.t. frac(qx) < frac(ux) < frac(sx) And therefore there exists a t, s.t. p+qx < t+ux < r+sx. (p,q,r,s,t,u integers, x irrational) To lift from mathworld: <<< A consequence of Weyl's criterion is that the sequence {frac(nx)} is dense and equidistributed in the interval [0,1) for irrational x, where n = 1, 2, ... (Finch 2003). ... Finch, S. R. "Powers of 3/2 Modulo One." ยง2.30.1 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 194-199, 2003.
Phil ===== When inserting a CD, hold down shift to stop the AutoRun feature In the Device Manager, disable the SbcpHid device. http://www.cs.princeton.edu/~jhalderm/cd3/ __________________________________ Do you Yahoo!? Yahoo! Mail - 50x more storage than other providers! http://promotions.yahoo.com/new_mail